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[D] How to compute the “true” posterior for a generative model?

I have seen a few papers that show plots of the “true posterior” for a generative model on a toy problem.

Before I did not understand how this could be computed, but now maybe I am closer. I’m sure you can help me

Is this the way to do it? (See below)

Definitions and setup:

The generative model is p(x|z)*p(z). The posterior is p(z|x).

A particular x is given and we want to know the distribution p(z|x) for that x,

using p(z|x) ~ p(x|z)*p(x) ,

i.e. without evaluate the Bayes denominator.

  1. Sample z from p(z),
  2. evaluate p(x|z) for the given x, and multiply this by p(z) for the z that was sampled in step 1. This gives an “unnormalized” probability for this particular z.
  3. Accept this new z as a sample using MCMC, e.g. metropolis-hasting.
  4. Repeat 1-3, and then eventually make a kernel density plot of the resulting z sample locations.

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Toronto AI is a social and collaborative hub to unite AI innovators of Toronto and surrounding areas. We explore AI technologies in digital art and music, healthcare, marketing, fintech, vr, robotics and more. Toronto AI was founded by Dave MacDonald and Patrick O'Mara.